Yes but you could just as easily hang it in a filter sock or a brand new pantyhose. What would work even better/faster would be actual filter media. Any reason you can't steal some filter floss or foam from your established tank and throw it in the new filter? Even if it isn't made for the other filter, you can usually make it fit with some persuasion.
Shrimp will not put enough of a bioload out to get your ammonia levels up. If you are doing a fish-in cycle I would recommend doing it with something hardier than a shrimp. Be prepared for lots of water changes too!
Barbs would be a good choice, IMO. I never had much luck with neons. I've probably owned 30+ in my years of keeping them and I don't think any lived over a couple years.